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# MCQ in Algebra and General Mathematics Part 6 | ECE Board Exam

This is the Multiple Choice Questions Part 6 of the Series in Algebra and General Mathematics topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

• MCQ in Algebraic functions | MCQ in theory of Equations | MCQ in Factorization and Algebraic functions | MCQ in Ratio, Proportion and Variation | MCQ in Matrix theory | MCQ in Arithmetic and Geometric Progression | MCQ in Equations and Inequalities | MCQ in Linear and Quadratic Equations | MCQ in Complex Number System | MCQ in Polynomials | MCQ in Mathematical Induction | MCQ in Logic and Probability | MCQ in Statistics| MCQ in System of Numbers and Conversion | MCQ in Fundamentals in Algebra | MCQ in Binomial Theorems and Logarithms | MCQ in Age Problems | MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Motion Problems | MCQ in Clock Problems | MCQ in Variation | MCQ in Progression | MCQ in Miscellaneous Problems

#### Continue Practice Exam Test Questions Part 6 of the Series

Choose the letter of the best answer in each questions.

251. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2

a. 1/3

b. 1/2

c. 3/4

d. 1/4

Solution:

252. If equal spheres are piled in the form of a complete pyramid with an equilateral triangles as base, find the total number of spheres in the pile if each side of the base contains 4 spheres.

a. 15

b. 20

c. 18

d. 21

Solution:

253. Find the 6th term of the sequence 55, 40, 28, 19, 13โฆ.

a. 10

b. 9

c. 8

d. 11

Solution:

254. In the series 1, 1, 1/2, 1/6, 1/24โฆ determine the 6th term

a. 1/80

b. 1/74

c. 1/100

d. 1/120

Solution:

255. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point

a. 8

b. 1

c. 7

d. 5

Solution:

256. In a class of 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry?

a. 10

b. 11

c. 12

d. 13

Solution:

257. A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both?

a. 10

b. 11

c. 12

d. 13

Solution:

258. A survey of 100 persons revealed that 72 of them had each at restaurant P and that 52 of them had eaten at restaurant Q. which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q?

a. 20

b. 22

c. 24

d. 26

Solution:

259. The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and for the subject Communications is 5/7. If none of the examinees fails both subject and there are 4 examinees who pass both subjects, find the number of examinees from the school who took the examinations.

a. 20

b. 25

c. 30

d. 28

Solution:

260. In a commercial survey involving 1000 persons on brand preference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x and 370 prefer either z or x but not y. How many persons have no brand preference, satisfied with any of the three brands?

a. 280

b. 230

c. 180

d. 130

Solution:

261. A toothpaste firm claims that in a survey of 54 people, they were using either Colgate, Hapee of Close-up brand. The following statistics were found: 6 people used all three brands, 5 used only Hapee and Close-up, 18 used Hapee or Close-up, 2 used Hapee, 2 used only Hapee and Colgate, 1 used Close-up and Colgate, and 20 used only Colgate. Is the survey worth paying for?

a. Neither yes or no

b. Yes

c. No

d. Either yes or no

Solution:

262. How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word โpersonnelโ?

a. 40

b. 480

c. 20

d. 312

Solution:

263. Five different mathematics books, 4 different electronics books and 2 different communications books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed.

a. 292

b. 5760

c. 34560

d. 12870

Solution:

264. The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is

a. 144

b. 258

c. 720

d. 450

Solution:

265. If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win first, second, third, fourth and fifth prizes?

a. 4,845

b. 116,260

c. 360,360

d. 3,003

Solution:

266. How many 4 digit numbers can be formed without repeating any digits from the following digits: 1, 2, 3, 4 and 6?

a. 120

b. 130

c. 140

d. 150

Solution:

267. How many permutations are there if the letters PNRCSE are taken six at a time?

a. 1440

b. 480

c. 720

d. 360

Solution:

268. In how many ways can 6 distinct books be arranged in a bookshelf?

a. 720

b. 120

c. 360

d. 180

Solution:

269. What is the number of permutations of the letters in the word BANANA?

a. 36

b. 60

c. 52

d. 42

Solution:

270. A PSME unit has 10 MEโs, 8 PMEโs and 6 CPMโs. If a committee of 3 members, one from each group is to be formed, how many such committees can be formed?

a. 2,024

b. 12,144

c. 480

d. 360

Solution:

271. In how many ways can a PSME Chapter with 15 directors choose a President, a Vice-President, a Secretary, a Treasurer and an Auditor, if no member can hold more than one position?

a. 360,360

b. 32,760

c. 3,003

d. 3,603,600

Solution:

272. Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags?

a. 64

b. 66

c. 68

d. 62

Solution:

273. In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?

a. 1152

b. 2304

c. 576

d. 2204

Solution:

274. There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example if a white and red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible?

a. 24

b. 6

c. 12

d. 36

Solution:

275. How many different ways can 5 boys and 5 girls form a circle with boys and girls alternate?

a. 28,800

b. 2,880

c. 5,600

d. 14,400

Solution:

276. There are four balls of different colors. Two balls at a time are taken and arranged any way. How many such combinations are possible?

a. 36

b. 3

c. 6

d. 12

Solution:

277. How many 6-number combinations can be generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers?

a. 850,668

b. 5,245,786

c. 188,848,296

d. 31,474,716

Solution:

278. Find the total number of combinations of three letters J, R, T taken 1, 2, 3 at a time

a. 7

b. 8

c. 9

d. 10

Solution:

279. In how many ways can you invite one or more of your five friends in a party?

a. 15

b. 31

c. 36

d. 25

Solution:

280. In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers?

a. 18

b. 64

c. 32

d. None of these

Solution:

281. In Mathematics examination, a student may select 7 problems from a set of 10 problems. In how many ways can he make his choice?

a. 120

b. 530

c. 720

d. 320

Solution:

282. How many committees can be formed by choosing 4 men from an organization of a membership of 15 men?

a. 1390

b. 1240

c. 1435

d. 1365

Solution:

283. A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose 9 men and 6 women who qualified for the position?

a. 680

b. 540

c. 480

d. 840

Solution:

284. There are 13 teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they play without any team playing more than one game in any day?

a. 11

b. 12

c. 13

d. 14

Solution:

285. There are five main roads between the cities A and B, and four between B and C. in how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice?

a. 260

b. 240

c. 120

d. 160

Solution:

286. There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets?

a. 50%

b. 25%

c. 20%

d. 40%

Solution:

287. Roll a pair of dice. What is the probability that the sum of two numbers is 11?

a. 1/36

b. 1/9

c. 1/18

d. 1/20

Solution:

288. Roll two dice once. What is the probability that the sum is 7?

a. 1/6

b. 1/8

c. 1/4

d. 1/7

Solution:

289. In a throw of two dice, the probability of obtaining a total of 10 or 12 is

a. 1/6

b. 1/9

c. 1/12

d. 1/18

Solution:

290. Determine the probability of drawing either a king or a diamond in a single draw from a pack of 52 playing cards.

a. 2/13

b. 3/13

c. 4/13

d. 1/13

Solution:

291. A card is drawn from a deck of 52 playing cards. Find the probability of drawing a king or red card.

a. 0.5835

b. 0.5385

c. 0.3585

d. 0.8535

Solution:

292. A coin is tossed 3 times. What is the probability of getting 3 tails up?

a. 1/8

b. 1/16

c. 1/4

d. 7/8

Solution:

293. The probability of getting at least 2 heads when a coin is tossed four times is

a. 11/16

b. 13/16

c. 1/4

d. 3/8

Solution:

294. A fair coin is tossed three times. What is the probability of getting either 3 heads or 3 tails?

a. 1/8

b. 3/8

c. 1/4

d. 1/2

Solution:

295. The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit?

a. 19/27

b. 8/27

c. 2/3

d. 1/3

Solution:

296. There are 3 questions in a test. For each question 1 point is awarded for a correct answer and none for a wrong answer. If the probability that Janine correctly answers a question in the test is 2/3, determine the probability that she gets zero in the test.

a. 8/27

b. 4/9

c. 1/30

d. 1/27

Solution:

297. In the ECE Board Examinations, the probability that an examinee will pass each subject is 0.8. What is the probability that an examinee will pass at least two subjects out of the three board subjects?

a. 70.9%

b. 80.9%

c. 85.9%

d. 89.6%

Solution:

298. In a multiple choice test, each question is to be answered selecting 1 out of 5 choices, of which only 1 is right. If there are 10 questions in a test, what is the probability of getting 6 right of pure guesswork?

a. 10%

b. 6%

c. 0.44%

d. 0.55%

Solution:

299. From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is drawn at random. Determine the probability that it is red or white.

a. 1/3

b. 7/12

c. 5/12

d. 1/4

Solution:

300. From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that both balls are white. Assume that the first ball is returned before the second ball is drawn.

a. 25/81

b. 16/81

c. 5/18

d. 40/81

Solution:

301. A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?

a. 5/16

b. 5/28

c. 5/32

d. 5/14

Solution:

302. A urn contains 4 black balls and 6 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws from the urn?

a. 0.24

b. 0.27

c. 0.53

d. 0.04

Solution:

303. From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that one ball is white and one ball is black. Assume that the first ball is returned before the second ball is drawn.

a. 16/81

b. 25/81

c. 20/18

d. 40/81

Solution:

304. A group of 3 people enter a theater after the lights had dimmed. They are shown to the correct group of 3 seats by the usher. Each person holds a number stub. What is the probability that each is in the correct seat according to the numbers on seat and stub

a. 1/6

b. 1/4

c. 1/2

d. 1/8

Solution:

305. From 20 tickets marked with the first 20 numerals, one is drawn at random. What is the chance that it will be a multiple of 3 or of 7?

a. 1/2

b. 8/15

c. 3/10

d. 2/5

Solution:

### Online Questions and Answers in Algebra and General Mathematics Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Algebra and General Mathematics
PART 1: MCQ from Number 1 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                          Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                        Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                         Answer key: PART 5
PART 6: MCQ from Number 251 โ 300                         Answer key: PART 6
PART 7: MCQ from Number 301 โ 350                         Answer key: PART 7
PART 8: MCQ from Number 351 โ 400                         Answer key: PART 8
PART 9: MCQ from Number 401 โ 450                         Answer key: PART 9
PART 10: MCQ from Number 451 โ 500                        Answer key: PART 10

### Online Questions and Answers in Fundamentals in Algebra Series

Following is the list of practice exam test questions in this brand new series:

MCQ in Fundamentals in Algebra
PART 1: MCQ from Number 1 โ 50                           Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                      Answer key: PART 2

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